def get_irrep_matrices(path, io):
DG_std = path.distortion_group.std_matrices
io.print("\n\nIrrep. #" + str(io.irr_num) + " chosen...")
if io.irr_num != 0:
irrep_tools = IrrepTools()
irrep = irrep_tools.get_irrep(group_data=DG_std,
stokes_number=io.irr_num,
dimension=io.irr_dim,
k_params=(None, None, None))
else:
raise ValueError("No irrep chosen.")
io.print("\n\n")
io.print("------- Irrep. Matrices:\n")
for j in range(0, len(irrep)):
irrep_matrix = irrep.irrep_matrices[j].matrix
io.print("Symmetry Element " + str(j + 1) + " : \n" +
str(irrep_matrix) + "\n")
return irrep
def test_get_irrep_mat():
stokes_number = 7611
dimension = 3
symmop = SymmOp([[0, 3, 0, -1], [-3, 3, 0, 1], [0, 0, -3, 1], [0, 0, 0,
3]])
irr = IrrepTools()
irrep_mat = irr.get_irrep_mat(stokes_number=stokes_number,
dimension=dimension,
symmop=symmop)
assert irrep_mat.matrix.tolist() == [[0, 0, -1], [-1, 0, 0], [0, 1, 0]]
assert irrep_mat.label == "F1+"
def test_get_irrep_mat(self):
stokes_number = 7611
dimension = 3
symmop = SymmOp([[0, 3, 0, -1], [-3, 3, 0, 1],
[0, 0, -3, 1], [0, 0, 0, 3]])
irr = IrrepTools()
irrep_mat = irr.get_irrep_mat(
stokes_number=stokes_number,
dimension=dimension,
symmop=symmop)
self.assertEqual(irrep_mat.matrix.tolist(), [
[0, 0, -1], [-1, 0, 0], [0, 1, 0]])
self.assertEqual(irrep_mat.label, 'F1+')
def get_irrep_matrices(path, io):
DG_std = path.distortion_group.std_matrices
if io.irr_num != 0:
irrep_tools = IrrepTools()
irrep = irrep_tools.get_irrep(group_data=DG_std,
stokes_number=io.irr_num,
dimension=io.irr_dim,
k_params=(None, None, None))
else:
raise ValueError("No irrep chosen.")
return irrep
def print_irreps(iso_sg_name,io):
io.print ("\n-------\n------- Possible irreps of the distortion group:\n-------\n")
out_text = IrrepTools.possible_irreps(iso_sg_name)
io.print(out_text)
def test_get_irrep(self):
stokes_number = 2857
dimension = 1
matrices = [[[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]],
[[-1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, 1.0]],
[[-1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]],
[[1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, 1.0]],
[[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]],
[[-1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, 1.0]],
[[-1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, 1.0]],
[[1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, 1.0]],
[[-1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, -1.0]],
[[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, -1.0]],
[[1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, -1.0]],
[[-1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, -1.0]],
[[-1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, -1.0]],
[[1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, -1.0]],
[[1.0, 0.0, 0.0],
[0.0, -1.0, 0.0],
[0.0, 0.0, -1.0]],
[[-1.0, 0.0, 0.0],
[0.0, 1.0, 0.0],
[0.0, 0.0, -1.0]]]
vectors = [[0.0, 0.0, 0.0],
[1.0, 0.0, 0.5],
[1.0, 0.0, 0.0],
[0.0, 0.0, 0.5],
[0.5, -0.5, 0.0],
[1.4999999959999997, -0.4999999999999998, 0.5],
[1.4999999959999997, -0.5, 0.0],
[0.5, -0.4999999999999998, 0.5],
[1.0, 0.0, 0.0],
[0.0, 0.0, 0.4999868850768938],
[0.0, 0.0, 0.0],
[1.0, 0.0, 0.4999868850768938],
[1.4999998980000022, -0.5, 0.0],
[0.5, -0.5, 0.4999868850768938],
[0.5, -0.5, 0.0],
[1.4999998980000022, -0.5, 0.4999868850768938]]
group_data = []
for entry in range(len(matrices)):
group_data.append(SymmOp.from_rotation_and_translation(rotation_matrix=matrices[entry],
translation_vec=vectors[entry]))
ir_mat_data = [[[1]], [[-1]], [[-1]], [[1]], [[-1]], [[1]], [[1]], [[-1]],
[[1]], [[-1]], [[-1]], [[1]], [[-1]], [[1]], [[1]], [[-1]]]
irr = IrrepTools()
irrep = irr.get_irrep(group_data=group_data, stokes_number=stokes_number,
dimension=dimension, k_params=(None, None, None))
irmats = irrep.irrep_matrices
for op_num in range(len(irmats)):
self.assertEqual(irmats[op_num].matrix, ir_mat_data[op_num])
self.assertEqual(irrep.label, 'Y4+')
def gen_perturb(path, irrep, io):
images = path.images
DG = path.distortion_group.matrices
num_unstar = path.distortion_group.num_unstar
numIm = len(images)
irrep_tools = IrrepTools()
# -- Generate starting basis
atoms1 = images[0].frac_coords
numAtoms = len(atoms1)
basis = np.zeros(numAtoms)
atoms2 = images[numIm - 1].frac_coords
m_vec = np.dot(np.linalg.inv(images[0].lattice.matrix),
[io.min_move, io.min_move, io.min_move])
for i in range(0, numAtoms):
if not closewrapped(atoms1[i, :], atoms2[i, :], m_vec):
basis[i] = 1
# -- Generate matrix showing atom mapping for each operations
a_map = path.gen_atom_map(basis=basis, vectol=io.vectol)
# -- Generate and apply modes for an irrep of arbitrary dimension
pt = np.zeros((numIm, numAtoms, 3))
pt_mode_init = irrep_tools.projection_diag(images=images,
symmop_list=DG,
irrep=irrep,
num_unstar=num_unstar,
a_map=a_map,
basis=basis)
if not np.any(pt_mode_init):
raise RuntimeError(
f"Uniform random initial perturbation does not contain any non-zero contributions from irrep {irrep.stokes_number}.\
Try a different irrep.")
pt_mode_init = pt_mode_init / np.linalg.norm(
np.ndarray.flatten(pt_mode_init))
pt += io.m_co[0] * pt_mode_init
if io.irr_dim > 1:
for i in range(1, io.irr_dim):
pt_mode = irrep_tools.projection_odiag(
images=images,
symmop_list=DG,
num_unstar=num_unstar,
irrep=irrep,
vec=pt_mode_init,
index=i,
a_map=a_map,
basis=basis,
)
pt += io.m_co[i] * (pt_mode /
np.linalg.norm(np.ndarray.flatten(pt_mode)))
p_vec = [
io.p_mag / np.linalg.norm(images[0].lattice.matrix[m, :])
for m in range(0, 3)
]
# print pt[3]/np.amax(abs(pt[3]))
# print(np.amax(p_vec*(pt[:,:,:]/np.amax(abs(pt)))))
images_alt = []
for i in range(numIm):
image_copy = images[i].copy()
alt_species = image_copy.species
perturbed_coords = image_copy.frac_coords + p_vec * (pt[i, :, :] /
np.amax(abs(pt)))
for j in range(numAtoms):
image_copy.replace(j, alt_species[j], perturbed_coords[j])
images_alt.append(image_copy)
return images_alt, basis
def gen_perturb(path, irrep, io):
images = path.images
DG = path.distortion_group.matrices
num_unstar = path.distortion_group.num_unstar
numIm = len(images)
irrep_tools = IrrepTools()
io.print("\n\n\n\n" + ("=" * 27 + "\n") * 2 +
"\nGenerating perturbations...\n\n" + ("=" * 27 + "\n") * 2 +
"\n")
io.print("***THE FOLLOWING DATA IS FOR THE PERTURBED IMAGES***\n\n")
# -- Generate starting basis
atoms1 = images[0].frac_coords
numAtoms = len(atoms1)
basis = np.zeros(numAtoms)
atoms2 = images[numIm - 1].frac_coords
m_vec = np.dot(np.linalg.inv(images[0].lattice.matrix),
[io.min_move, io.min_move, io.min_move])
for i in range(0, numAtoms):
if not closewrapped(atoms1[i, :], atoms2[i, :], m_vec):
basis[i] = 1
io.print("------- Atoms included in basis:")
symbols = images[0].species
for i in range(0, numAtoms):
if basis[i] == 0:
io.print(str(symbols[i]) + " No")
else:
io.print(str(symbols[i]) + " Yes")
# -- Generate matrix showing atom mapping for each operations
a_map = path.gen_atom_map(basis=basis, vectol=io.vectol)
# -- Generate and apply modes for an irrep of arbitrary dimension
pt = np.zeros((numIm, numAtoms, 3))
pt_mode_init = irrep_tools.projection_diag(images=images,
symmop_list=DG,
irrep=irrep,
num_unstar=num_unstar,
a_map=a_map,
basis=basis)
pt_mode_init = pt_mode_init / \
np.linalg.norm(np.ndarray.flatten(pt_mode_init))
pt += io.m_co[0] * pt_mode_init
if io.irr_dim > 1:
for i in range(1, io.irr_dim):
pt_mode = irrep_tools.projection_odiag(images=images,
symmop_list=DG,
num_unstar=num_unstar,
irrep=irrep,
vec=pt_mode_init,
index=i,
a_map=a_map,
basis=basis)
pt += io.m_co[i] * \
(pt_mode/np.linalg.norm(np.ndarray.flatten(pt_mode)))
p_vec = [
io.p_mag / np.linalg.norm(images[0].lattice.matrix[m, :])
for m in range(0, 3)
]
# print pt[3]/np.amax(abs(pt[3]))
# print(np.amax(p_vec*(pt[:,:,:]/np.amax(abs(pt)))))
images_alt = []
for i in range(numIm):
image_copy = images[i].copy()
alt_species = image_copy.species
perturbed_coords = image_copy.frac_coords + p_vec * (pt[i, :, :] /
np.amax(abs(pt)))
for j in range(numAtoms):
image_copy.replace(j, alt_species[j], perturbed_coords[j])
images_alt.append(image_copy)
return images_alt